solve for x:

and could you show me the step on how to do it? thank u!

1) 5.8 = .17x(sqaured)+.95x + 5.68

2) 5.8 = .09x(squared) + .01x (cubed) + 1.1x + 5.64

1) is an example of a quadratic equation in standard form. One could factor, complete the square, or use the quadratic formula. It would be messy, however.

2) Do you have access to a graphing calculator? Are you expected to do this one by hand? What math class are these for?

Do you know how to do synthetic or long division of polynomials? The basic idea is that you can find zeroes which would tell you where the x intercepts of the graph are. Trust me this far: Always put the right side of the equals sign in descending order of exponents (cubed first, next comes squared, then comes just plain x which is to the first power anyway, and then the numerical coefficient goes last. The graph will bounce away at even points and cross at odd points. This is all I can remember at this point. Someone else should be able to help you further. I will try to dig through my brain and remember more.

As Brandon stated, the first one can be done by using the quadratic equation formula

for the second, I would multiply each term by 100 and simplify to get

x^3 + 9x^2 + 110x - 16 = 0

and then use a "calculator" like
http://www.1728.com/cubic.htm

enter the coefficients to get one real and two complex roots.

I followed the link you gave and clicked on their method for solving these that is located on the very bottom of the page. Boy, that is an arduous process! I forgot about clearing decimals and setting one side of the equation to zero. Talk about obvious oversights on my part! In this sense, complex means consisting of both a real portion as well as an imaginary (or "unreal") part. Instead of relying on shortcuts for instant gratification, I would suggest that she actually learn some of the procedures that I listed above.

Sure, I can help you solve these equations for x and explain the steps. Let's start with the first equation:

1) 5.8 = 0.17x^2 + 0.95x + 5.68

Step 1: Rearrange the equation to bring all terms to one side, set it equal to zero:
0.17x^2 + 0.95x + 5.68 - 5.8 = 0

Step 2: Combine like terms:
0.17x^2 + 0.95x - 0.12 = 0

Step 3: It's best to work with whole numbers, so we can multiply the entire equation by 100 to eliminate the decimal:
100(0.17x^2 + 0.95x - 0.12) = 100(0)

Step 4: Distribute the multiplication:
17x^2 + 95x - 12 = 0

Step 5: Now we have a quadratic equation, we can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / 2a

In this equation, a = 17, b = 95, and c = -12.

Step 6: Substitute the values into the quadratic formula:
x = (-95 ± √(95^2 - 4 * 17 * -12)) / (2 * 17)

Step 7: Simplify the equation:
x = (-95 ± √(9025 + 816)) / 34
x = (-95 ± √9831) / 34

Step 8: Use a calculator to find the square root of 9831 and evaluate both solutions separately:
x ≈ 1.509 or x ≈ -6.675

So the solutions for the equation 1) are approximately x = 1.509 and x = -6.675.

Now let's move on to the second equation:

2) 5.8 = 0.09x^2 + 0.01x^3 + 1.1x + 5.64

Step 1: Rearrange the equation to bring all terms to one side, set it equal to zero:
0.01x^3 + 0.09x^2 + 1.1x - 0.16 = 0

Step 2: Multiply the entire equation by 100 to eliminate the decimal:
100(0.01x^3 + 0.09x^2 + 1.1x - 0.16) = 100(0)

Step 3: Distribute the multiplication:
x^3 + 9x^2 + 110x - 16 = 0

Step 4: You can try different methods to solve cubic equations. One common method is to graph the equation and find the x-intercepts. Another method is to use numerical methods such as Newton's method or the bisection method to approximate the solutions.

For this equation, without using advanced numerical methods, it might be difficult to find the exact solutions algebraically. Therefore, using a graphing calculator or numerical methods would be recommended.

I hope this helps you understand the process of solving these equations. If you have any further questions, feel free to ask!